(Ebook) Advanced Engineering Mathematics 6th Edition by Peter Neil ISBN 9780495082378 0495082376

(Ebook) Advanced Engineering Mathematics 6th Edition by Peter Neil ISBN 9780495082378 0495082376

(Ebook) Advanced Engineering Mathematics 6th Edition  by Peter V. O'Neil  - Ebook PDF Instant Download/Delivery:  9780495082378,  0495082376
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Product details: 

ISBN 10: 0495082376

ISBN 13:  9780495082378

Author: Peter V. O'Neil
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Table of contents: 

Part I. Ordinary Differential Equations
Chapter 1. First-Order Differential Equations

1.1 Preliminary Concepts

1.1.1 General and Particular Solutions

1.1.2 Implicitly Defined Solutions

1.1.3 Integral Curves

1.1.4 The Initial Value Problem

1.1.5 Direction Fields

1.2 Separable Equations

1.2.1 Applications of Separable Differential Equations

1.3 Linear Differential Equations

1.4 Exact Differential Equations

1.5 Integrating Factors

1.5.1 Separable Equations and Integrating Factors

1.5.2 Linear Equations and Integrating Factors

1.6 Homogeneous, Bernoulli, and Riccati Equations

1.6.1 Homogeneous Differential Equations

1.6.2 The Bernoulli Equation

1.6.3 The Riccati Equation

1.7 Applications to Mechanics, Electrical Circuits, and Orthogonal Trajectories

1.7.1 Mechanics

1.7.2 Electrical Circuits

1.7.3 Orthogonal Trajectories

1.8 Existence and Uniqueness for Solutions of Initial Value Problems

Chapter 2. Second-Order Differential Equations

2.1 Preliminary Concepts

2.2 Theory of Solutions of 

2.2.1 The Homogeneous Equation

2.2.2 The Nonhomogeneous Equation

2.3 Reduction of Order

2.4 The Constant-Coefficient Homogeneous Linear Equation

2.4.1 Case 1

2.4.2 Case 2

2.4.3 Case 3

2.4.4 Alternative General Solution in the Complex Root Case

2.5 Euler’s Equation

2.6 The Nonhomogeneous Equation

2.6.1 Variation of Parameters

2.6.2 Undetermined Coefficients

2.6.3 Superposition

2.6.4 Higher-Order Differential Equations

2.7 Applications to Mechanical Systems

2.7.1 Unforced Motion

2.7.2 Forced Motion

2.7.3 Resonance

2.7.4 Beats

2.7.5 Analogy with an Electrical Circuit

Chapter 3. The Laplace Transform

3.1 Definition and Basic Properties

3.2 Solving Initial Value Problems

3.3 Shifting Theorems and the Heaviside Function

3.3.1 First Shifting Theorem

3.3.2 Heaviside Function and Pulses

3.3.3 Second Shifting Theorem

3.3.4 Electrical Circuit Analysis

3.4 Convolution

3.5 Unit Impulses and the Dirac Delta Function

3.6 Systems via Laplace Transform

3.7 Differential Equations with Polynomial Coefficients

Chapter 4. Series Solutions

4.1 Power Series Solutions of IVPs

4.2 Recurrence Relations

4.3 Singular Points and the Frobenius Method

4.4 Second Solutions and Logarithmic Factors

Chapter 5. Numerical Approximation of Solutions

5.1 Euler’s Method

5.1.1 Radioactive Waste Disposal Problem

5.2 One-Step Methods

5.2.1 Second-Order Taylor Method

5.2.2 Modified Euler Method

5.2.3 Runge–Kutta Methods

5.3 Multistep Methods

5.3.1 Case 

Part II. Vectors and Linear Algebra
Chapter 6. Vectors and Vector Spaces

6.1 Algebra and Geometry of Vectors

6.2 Dot Product

6.3 Cross Product

6.4 The Vector Space ℝⁿ

6.5 Linear Independence, Spanning Sets, and Dimension

Chapter 7. Matrices and Systems of Linear Equations

7.1 Matrices

7.1.1 Matrix Algebra

7.1.2 Matrix Notation for Linear Systems

7.1.3 Special Matrices

7.1.4 Rationale for Matrix Multiplication

7.1.5 Random Walks in Crystals

7.2 Elementary Row Operations and Matrices

7.3 Row Echelon Form

7.4 Row/Column Spaces and Rank

7.5 Homogeneous Systems

7.6 Solution Space of 

7.7 Nonhomogeneous Systems

7.7.1 Structure of Solutions

7.7.2 Existence and Uniqueness

7.8 Matrix Inverses

7.8.1 Finding 

Chapter 8. Determinants

8.1 Permutations

8.2 Definition

8.3 Properties

8.4 Evaluation via Row/Column Operations

8.5 Cofactor Expansions

8.6 Triangular Matrices

8.7 Determinant Formula for Inverse

8.8 Cramer’s Rule

8.9 The Matrix Tree Theorem

Chapter 9. Eigenvalues, Diagonalization, and Special Matrices

9.1 Eigenvalues and Eigenvectors

9.1.1 Gerschgorin’s Theorem

9.2 Diagonalization

9.3 Orthogonal and Symmetric Matrices

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Tags: Peter Neil, Advanced Engineering